Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models

Abstract

We conjecture the existence of hidden Onsager algebra symmetries in two interacting quantum integrable lattice models, i.e. spin-1/2 XXZ model and spin-1 Zamolodchikov-Fateev model at arbitrary root of unity values of the anisotropy. The conjectures relate the Onsager generators to the conserved charges obtained from semi-cyclic transfer matrices. The conjectures are motivated by two examples which are spin-1/2 XX model and spin-1 U(1)-invariant clock model. A novel construction of the semi-cyclic transfer matrices of spin-1 Zamolodchikov-Fateev model at arbitrary root of unity value of the anisotropy is carried out via transfer matrix fusion procedure.

arXiv comment32 pages, 3 figures

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• Integrable Quantum Circuits from the Star-Triangle Relation
• Popcorn Drude weights from quantum symmetry
• Pivoting through the chiral-clock family
• Rational Q-systems at Root of Unity I. Closed Chains
• Symmetry-Enforced Fermi Surfaces
• On the Q operator and the spectrum of the XXZ model at root of unity
• Parity anomaly from LSM: exact valley symmetries on the lattice